Effect of Coupling Types onRotor Vibration

Ronak Prajapati1Dr. Anand Parey2

1, 2Indian Institute ofTechnology IndoreMadhya Pradesh, India 453552

1me130003030@iiti.ac.in 2anandp@iiti.ac.in

AbstractCouplings are widely used in compressors, gas turbines, and aerospace applications because of their ability totransmit torque and their consequent ability to compensate misalignment in almost all directions. The basicfunction of a coupling is to transmit torque from the driver to the driven piece of rotating equipment. Thecoupling type and increase in shaft speed has a great influence on rotor vibration. Investigation of the factorsinfluencing the rotor vibrations due to coupling type and increase in shaft speed will help to improve the designand control of a rotor dynamic system. In the following pages, a 3D finite element (FE) model of a rotordynamic system is built with different coupling types i.e. Rigid, Jaw, Flexible Couplings. Based on this model,the effect of coupling type on natural frequencies of the system was observed. An experimental setup wasestablished with the help of Machine Fault Simulator to observe the change in vibration amplitude with couplingtypes and increase in shaft speed. The experimental results showed that coupling type greatly influenced thevibration amplitude and a trend was observed while increasing the shaft speed. Finally, conclusions weredelivered based on these results and further research scope was discussed.

1 Introduction

Due to the high speed of some rotating machinery, the need for a better understanding of the vibrationphenomena is becoming a necessity for practical engineers for the purpose of troubleshooting. Most rotatingequipment consists of a driver and driven machine coupled through a mechanical coupling. The mechanicalcoupling is used mainly to transmit torque from the driver to the driven machine. Due to current trends in thedesign of rotating machinery towards higher speeds and lower vibration manufacturers are tending to producemachines which operate closer to lateral critical speeds than has previously been necessary. Consequently, theeffect of coupling upon the higher speeds and misalignment on vibration amplitudes of such machines is be-coming an increasingly important consideration for rotor-bearing systems. The vibration in rotating machineryis mostly caused by unbalance, misalignment, mechanical looseness and other malfunctions. However, theperfect alignment between the driving and driven machines cannot be attained in real world. To ensure that therotor of a piece of rotating machinery is sufficiently designed to withstand the stresses and strains of the oper-ating environment, the coupling chosen to join the driving and driven mechanisms must be properly selected.In addition to transmitting torque from the driving to the driven pieces of machinery, the coupling must alsocompensate for all possible unintentional vibrations apart from misalignment of the rotating devices [1].M.Xu and Marangoni[2][3] have developed a theoretical model of a complete motor-flexible-coupling-rotorsystem using the component mode synthesis. General system of equation of motion derived for a system un-der misalignment and unbalance condition. The derived equations indicate that forcing frequency due to shaftmisalignment are even multiple frequencies of the motor rotational speed. They also validated their theoreticalresults with experimental study. A.Askarian,S.M.R. Hashemi[4] studied effect of axial force, unbalance andcoupling misalignment on vibration of rotor gas turbine. It is reported that for unbalance highest amplitude isat 1X of the shaft speed and for misalignment highest amplitude is at 2X of the shaft speed. V.Hariran ,P.S.S.Srinivasan[5] studied the effect of unbalance on a rotor system with flexible flange coupling. The experimen-tal and numerical spectra were obtained for unbalance under different unbalance forces. They concluded thatboth experimental and numerical results show the dominant peak at 1X and experimental results are in goodagreement with numerical results

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1.1 Couplings

Couplings are mechanical elements that couples two drive components which enables motion to be trans-ferred from one component to another. The drive components are generally shafts. We tend to see lot ofapplications of the couplings mainly in the automobiles sector, for example the drive shaft which connects theengine and the rear axle in a bus or any automobile is connected by means of a universal joint.As with all mechanical devices, a coupling must match its intended purpose and application parameters, includ-ing many different performance, environmental, use and service factors. All must be satisfied for the couplingto work properly. When selected with these design parameters in mind, and when installed and operating cor-rectly, a coupling should have no failure issues over it’s lifetime. However, when one or more of these is notmet a coupling can prematurely fail, resulting in either mahcine failure or injury to the operator of the coupledmachine. In order to transmit torque between two shafts that either tend to lie in the same line or slightly mis-aligned, a coupling is used. Based on the area of applications there are various types of coupling available.Butthey are generally categorized as:-1. Rigid Couplings2. Flexible or Compensating Couplings3. Miscellaneous Couplings

1.2 Effect of Coupling Type on Bearing Forces

As a coupling flexes, it generates forces at the shaft support bearings. But designers seldom considerthese forces (loads) when selecting couplings and bearings. The reaction forces may seem surprisingly highto engineers who never considered them before. In some equipment, especially delicate instruments that haveslender shafts running in fragile bearings, such forces can shorten the life of these bearings and shafts. Radialmisalignment of parallel shafts causes larger reaction forces than angular misalignment. [6]

1.2.1 Flexible couplings

The reaction, or resistance, of flexible couplings to radial (and angular) misalignment increases propor-tionally with shaft deflection. This reaction can be defined as a spring rate and expressed as force per unitdeflection. Because flexible couplings accommodate misalignment in a bending mode, reaction is proportionalto the flexing member thickness. In some types, such as the membrane and bellows couplings, the flexingmembers can be thin because torque is transmitted with the members in shear. Thus, high torsional stiffnessis attained with relatively low radial forces. Couplings with multiple flexing elements (beam and bellows) canalso use this approach, but generally require extensive modifications to divide the flexing elements into twoseparate clusters. Some short models are available that can be connected by an intermediate shaft .

1.2.2 Elastomeric couplings

Certain coupling types incorporate flexible elastomer elements and offer a range of torsional damping prop-erties. But their associated characteristics - relative rotation between hubs, and backlash - can be counter-productive in precision motion control applications. Depending on the coupling type, elastomer’s are loadedin shear, compression, bending, or combinations of these modes. One example of an elastomeric device, thejaw coupling is probably the most widely used general purpose coupling. This device transmits torque andaccommodates misalignment by compressing legs (or lobes) of an elastomeric insert between its jaws. As withflexural couplings, the reaction forces of elastomeric jaw couplings are proportional to radial shaft deflection.However, the ability of these couplings to handle radial misalignment and minimize bearing forces is generallyless than for other types. Therefore, the jaw coupling is best for applications where the connected shafts canbe manipulated into near alignment so as to keep bearing forces within an acceptable range. Softer elastomerinserts can be used to accommodate radial misalignment and minimize bearing forces. However, the trade-off isa commensurate reduction in torsional stiffness. Two jaw couplings mounted back-to-back will accommodateradial misalignment, but are rarely used this way, usually because of added cost.

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1.2.3 Rigid Couplings

The two elementary rigid coupling styles are machined set-screw, for smaller shafts, and ribbed, two-piececast, for larger and higher horsepower applications. The ribbed style, all but unchanged, remains the couplingof choice for large shafts, but it is uneconomical for shafts two inches or less in diameter. The machined,set-screw coupling is basically a cylinder with a key-way and set screws. From a simplistic viewpoint, this is asound design, but in practice its shortcomings become evident. It can loosen under vibration, and set screws canleave dents or dimples in the shaft or key-way, deforming the surface so that adjusting or removing the couplingbecomes difficult. While hardened, shafts may resist dents, they also can prevent set screws from locking andproperly holding in place. And with set-screw couplings, key-ways are necessary for torque transmission, thusthe phase relationship between coupled shafts cannot be changed. Clamping couplings dont damage the shaftsurface, they serve on hardened shafting, and they maintain hold under vibration and cyclic or reversing loads.Also, assembly and adjustment are not generally a problem. The coupling will clamp down around the shaftcircumference when the cap screws are tightened, and static friction between coupling and shaft keeps themturning together.This holding friction is influenced by the number of cap screws, the applied axial force along the each of thesescrews, and the coefficient of friction between contacting coupling and shaft surfaces. Axial screw force is afunction of screw thread lubrication and tightening torque, while the frictional coefficient is affected by thehardness, lubricity, and finish of contacting surfaces.However, the ability of these couplings to handle radial misalignment and minimize bearing forces is very lesscompared to Elastomeric and Flexible Couplings.

1.3 Modal Analysis

Modal analysis is used to determine the vibration characteristics of a structure, namely the natural frequen-cies and the mode shapes of the structure. The natural frequencies and mode shapes are important parametersin the design of a structure for dynamic loading conditions which determined by the inherent characteristicsand the materials of a structure. They are also required if you want to do a spectrum analysis or a mode super-position harmonic or transient analysis. By modal analysis on the rotor-bearing system we can get the responseof the structure withstands the different kinds of dynamic loads. On the one hand, the vibration characteristicsfor structure can be predicted. On the other hand, we can avoid the resonance phenomenon occurs in the designprocess, do the modification of the existing structure, and improve the reliability of the machine.

1.3.1 Modal Analysis Using FEM

For the most basic problem involving a linear elastic material which obeys Hooke’s Law, the matrix equa-tions take the form of a dynamic three-dimensional spring mass system. The generalized equation of motion isgiven as: [7]

[M][U ]+ [C][U ]+ [K][U ] = [F ]

where [M] is the mass matrix,[U] is the 2nd time derivative of the displacement [U] (i.e., the acceleration), [U]is the velocity, [C] is a damping matrix, [K] is the stiffness matrix, and [F] is the force vector. The generalproblem, with nonzero damping, is a quadratic eigenvalue problem. However, for vibrational modal analysis,the damping is generally ignored, leaving only the 1st and 3rd terms on the left-hand side:

[M][U ]+ [K][U ] = [0]

This is the general form of the eigensystem encountered in structural engineering using the FEM. To repre-sent the free-vibration solutions of the structure harmonic motion is assumed, [8] so that [U] is taken to equalλ [U ],where λ is an eigenvalue (with units of reciprocal time squared, e.g., s-2), and the equation reduces to: [9]

[M][U ]λ +[K][U ] = [0]

In contrast, the equation for static problems is:

[K][U ] = [F ]

which is expected when all terms having a time derivative are set to zero.

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1.4 Vibration Analysis

Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The oscilla-tions may be periodic, such as the motion of a pendulum-or random, such as the movement of a tire on a gravelroad. In many cases, however, vibration is undesirable, wasting energy and creating unwanted sound. For ex-ample, the vibrational motions of engines, electric motors, or any mechanical device in operation are typicallyunwanted. Such vibrations could be caused by imbalances in the rotating parts, uneven friction, or the meshingof gear teeth. Careful designs usually minimize unwanted vibrations. Vibration Analysis (VA), applied in anindustrial or maintenance environment aims to reduce maintenance costs and equipment downtime by detectingequipment faults. Most commonly VA is used to detect faults in rotating equipment (Fans, Motors, Pumps, andGearboxes etc.) such as Unbalance, Misalignment, rolling element bearing faults and resonance conditions. VAcan use the units of Displacement, Velocity and Acceleration displayed as a Time Waveform (TWF), but mostcommonly the spectrum is used, derived from a Fast Fourier Transform of the TWF. The vibration spectrumprovides important frequency information that can pinpoint the faulty component.

2 Setup

2.1 Modal Analysis

For Modal analysis in ANSYS Workbench, a 3D CAD Model(Fig. 1) of the system needs to be developedwith the help of a modelling software i.e. Solidworks 2013. Rotor shaft, Rotor, Motor Shaft and Couplingsare modeled using Soliworks 2013 with the exact dimensions(Fig. 2 and 3) as used in the experimental setup.The Couplings were designed from data available(Table 2) from manufacturer website. Material Properties ofeach component of the system(Table 3) needs to be acquired to replicate the stiffness and rigid behavior ofcomponents experiencing vibration.All the dimensions shown are in mm.

Figure 1: 2D Model of Rotor-Coupling System

Figure 2: 2D Model of Rotor [Side View]

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Figure 3: 2D Model of Rotor [Front View]

Item Dimension/mmRotor Shaft Diameter 19Motor Shaft Diameter 15.8

Table 1: Shaft Dimensions

Coupling Type Bore(mm) Torque(Nm) Max Speed(RPM) Length(mm)Max Min

Rigid 20 16 350 4000 65Flexible 19 16 21.47 10,000 63.5

Jaw 19 - 4.88 14,000 50.3

Table 2: Coupling Specifications

Item Material Density[g/cc] Poisson ratio Young’s ModulusRotor Shaft TGP 7.87 0.29 206 GPaMotor Shaft C45 Carbon Steel 7.85 0.29 210 GPa

Rotor Aluminium 2.6898 0.34 68.3 GPaRigid Coupling 1215 Carbon Steel 7.87 0.29 200 GPaJaw Coupling Sintered Iron 6.6 0.25 115 GPa

Spider (Jaw Coupling) Rubber 1 0.49 0.003 GPaFlexible Coupling Aluminium 2.6898 0.34 68.3 GPa

Table 3: Material Properties

2.2 Vibration Analysis

While analysis of a single machinery fault may be beneficial, there are many occasions when the analysis ofthe interaction between dynamic stiffness, resonance, and speed is essential in order to gain an understanding ofreal world vibration spectra. With the MFS, the expertise required to diagnose industrial machinery problemsin well controlled experiments can be developed and enhanced. With a plant running at full production, it isvirtually impractical to gain an understanding of the kinetics and dynamics of machinery without adverselyaffecting production and profits: The MFS enables offline training and experimentation which in turn willminimize production downtime.

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Figure 4: Experimental Setup

Fig 4 depicts the experimental setup to study the effect of coupling types on rotor vibration. It consists ofa DC motor, Jaw coupling and circular rotor on the shaft. The shaft of 19 mm diameter is supported by twoidentical rolling bearings. The bearing pedestals are provided in such a way as to adjust in vertical direction toalign the system or to create misalignment. The shaft is driven by a 1 HP DC motor. A 1 HP Variable Speedcontroller is used so that the system can be operated at different speeds.

A piezoelectric accelerometer manufactured by PCB PIEZOTRONICS (Type ICP, no 333B32) with 10.57mV/(m/s2) sensitivity is used along with the 4-Channel Vibration Analyser (OROS 34). The accelerometeris mounted on the bearing point with the help of wax provided with the kit. This accelerometer connects toOROS-34 with the help of 10-32 plug to BNC plug attached to a white 10-ft long FEP jacket coaxial cable. TheOROS 34 is connected with LAN to a Software Platform NVGate installed in the Laptop Cable, the vibrationsignal is recorded in NVGate, it hosts the suite of OROS software modules. The Recorder captures raw, time-domain data during your acquisition and analysis process. The Time Domain Signal obtained is converted toFrequency domain using FFT Analysis.

3 Methodology

3.1 Modal Analysis

The procedure for a modal analysis consists of four main steps:

• Build the model.

• Apply loads and obtain the solution.

• Expand the modes and Review the results.

Step 1. Build the modelBuilding a model in ANSYS means importing 3D CAD model into the Geometry Section of the schematic.Models imported from CAD systems may require extensive repair if they are not of suitable quality for meshing.

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Due to this, Geometry repair tools are used in the Geometry section for making the model meshing suitable.Material properties (i.e. Young’s Modulus, Poisson’s Ratio, and Density) of all components needs to be addedin Engineering Data Section. Apply Bearing support and assigning materials to all components.

Figure 5: System with bearing support

• Meshing

The procedure for generating a mesh of nodes and elements consists of three main steps:1. Set the element attributes.2. Set mesh controls. (ANSYS offers a large number of mesh controls, which you can choose from to suit yourneeds.)3. Generate the mesh.The second step, setting mesh controls, is not always necessary because the default mesh controls are appro-priate for many models. If no controls are specified, the program will use the default settings on the DESIZEcommand to produce a free mesh. As an alternative, you can use the SmartSize feature to produce a betterquality free mesh.

Figure 6: Meshed Couplings

Figure 7: Meshed Components

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Figure 8: Meshed System

Step 2. Apply Load and obtain solution.Apply loads, specify load step options, and Specify the number of modes to find (default is 6). Optionallyspecify a frequency search range (defaults from 0Hz to 1e+08Hz). Begin the finite element solution for thenatural frequencies. After the initial solution, you expand the mode shapes for review.Step 3. Expand the modes and Review the results.

Figure 9: System Under Free Vibration Mode

3.2 Vibration Analysis

Before recording the signals, the shaft is checked for alignment. Also, the surface level is checked by usingspirit level. The Sensitivity (i.e. 10.57mV/(m/s2)), Accelerometer type (i.e. ICP), Sampling Frequency (2.048kS/s), Channel no. are defined in the NVGate Software. The accelerometer should be checked before mountingat the Bearing1 by gently tapping the surface and checking the corresponding response in the NVGate software.The Accelerometer should be properly installed otherwise a loose attachment to the bearing housing will recordimproper signal and may distort the study of the signals.

Next, the vibration data is acquired using OROS 34 and recorded in laptop using NVGate software. A typ-ical vibration spectrum is acquired on Bearing1 for 500 RPM (8.3Hz) to study the behavior of vibration fre-quency spectrum at balanced condition with minimal misalignment. The speed is then increased to 1000 RPM(16.7Hz),1500 RPM (25Hz),2000 RPM (36.6Hz) using the 1 HP Variable Speed Controller. The vibration sig-nal is then recorded for each speed.

After acquiring spectrum for rigid coupling, the coupling is then changed and same procedure is followedfor jaw coupling and flexible coupling. While changing the coupling one must tighten the bearing housingsproperly and should run the system at 5 RPM to check the alignment of the tighten bearing housings.

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4 Results

4.1 FFT Analysis

1) At Speed=500 RPM, Sampling Frequency=2.048kS/s.

• Rigid Coupling

• Jaw Coupling

• Flexible Coupling

Figure 10: FFT Analysis for 500 RPM

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2) At Speed=1000 RPM, Sampling Frequency=2.048kS/s.

• Rigid Coupling

• Jaw Coupling

• Flexible Coupling

Figure 11: FFT Analysis for 1000 RPM

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2) At Speed=1500 RPM, Sampling Frequency=2.048kS/s.

• Rigid Coupling

• Jaw Coupling

• Flexible Coupling

Figure 12: FFT Analysis for 1500 RPM

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2) At Speed=1000 RPM, Sampling Frequency=2.048kS/s.

• Rigid Coupling

• Jaw Coupling

• Flexible Coupling

Figure 13: FFT Analysis for 2000 RPM

4.2 Modal Analysis

System Natural Frequency(Hz)Rigid Coupling 20.428Jaw Coupling 17.381

Flexible Coupling 8.0428

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5 Discussion

The results of modal analysis show that with different coupling type the natural frequency of the systemchanges due to change in mode shape.

1)The vibration amplitude of rigid coupling increases suddenly at 1000 RPM and then decreases at 1500 RPMand follows a slow increasing pattern afterwards.

2)The vibration amplitude of jaw coupling increases at 1000 RPM and then decreases gradually and almostbecomes constant.

3)The vibration amplitude of flexible coupling is the lowest of all which increases at 1000 RPM and startsdecreasing after 1500 RPM.

4)The Trend Graph obtained is: -

Figure 14: Vibration Trend Graph

6 Conclusion

Rigid coupling is more prone to vibrations as compared to jaw and flexible coupling. In Jaw coupling, thevibration level experienced is less compared to rigid coupling but more than flexible coupling. The flexiblecoupling can resist the vibration due to increase in shaft speed in better way. A trend of vibration amplitudeobserved as Rigid>Jaw>Flexible Coupling at all 4 Speeds.

By Introducing misalignment in a controlled manner, cases with angular and parallel can be performed toget an estimate of rotor vibration trend in each coupling assembly with increase in speed and to predict whichcoupling is more reliable in such cases. By Introduction of mass unbalance the vibration amplitudes of all the3 couplings can also be observed. All 3 couplings can be manufactured with the same material to conclude ifthe effect of coupling design prevails the effect of different coupling material on the vibration amplitude of thesystem

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References

[1] A.S. SEKHAR AND B.S. PRABHU, Effects of Coupling Misalignment on Vibrations of Rotating Machin-ery, Journal of Sound and Vibration (1995) 185(4),655-671.

[2] M.XU AND R.D. MARANGONI, Vibration Analysis of Motor-Flexible Coupling-Rotor System Subjectto Misalignment and Unbalance, Part-I:Theoretical Model and Analysis, Journal of Sound and Vibration,(1994), pg.663-679.

[3] M.Xu AND R.D. Marangoni, Vibration Analysis of Motor-Flexible Coupling-Rotor System Subject toMisalignment and Unbalance, Part-II: Experimental Validation, Journal of Sound and Vibration, (1994),pg.681-691.

[4] ABDOLREZAASKARIAN AND S.M.R. HASHEMI, Effect of axial force, unbalance and coupling mis-alignment on vibration of a rotor gas turbine, 14th international congress on sound vibration, CairnsAustralia, 2007.

[5] V. HARIHARAN AND P.S.S.SRINIVASAN, Vibration analysis of flexible coupling by considering unbal-ance, World applied sciences journal(8),2010.

[6] WALLY WALDEN, Huco Engineering Industries Ltd., Motion System Design, Oct 1, 2000

[7] CLOUGH, RAY W. , JOSEPH PENZIEN, Dynamics of Structures, 2nd Ed., McGraw-Hill PublishingCompany, New York, 1993, page 173

[8] BATHE ,KLAUS JURGEN, Finite Element Procedures, 2nd Ed., Prentice-Hall Inc., New Jersey, 1996,page 786

[9] CLOUGH, RAY W. AND JOSEPH PENZIEN Dynamics of Structures, 2nd Ed., McGraw-Hill PublishingCompany, New York, 1993, page 201

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